Trump on Israeli-Palestinian deal: 'We will get it done'
Trump made the comments after welcoming Abbas to the White House for talks aimed at relaunching the moribund peace process.
"I've always heard that perhaps the toughest deal to make is the deal between the Israelis and the Palestinians," Trump said.
"Let's see if we can prove them wrong. We will get it done," he said.
Abbas echoed Trump's upbeat tone, saying, "We believe that we can... be true partners to you to bring about a historic peace under your stewardship."
The US president greeted Abbas on the White House lawn before entering the Oval Office for talks, barely two months after receiving Israeli Prime Minister Binyamin Netanyahu.
In February, Trump renounced support for a Palestinian state and vowed to move the US embassy to Jerusalem, breaking two tenets of American policy held for decades.
At the same time, Trump has urged Israel to hold back on settlement building in the West Bank, a longstanding concern of Palestinians and the international community.
Since then, Israel has officially sanctioned the first new settlement in the occupied West Bank in over 25 years.
Palestinians are watching the meeting between Abbas and Trump closely, including the leader of the Hamas movement Khaled Meshaal, who called on Trump to break with past approaches to Middle East peace.
"This is a historic opportunity to pressure Israel... to find an equitable solution for the Palestinian people," he told CNN.
The United States has for several decades played a mediating role in the Israeli-Palestinian conflict, while remaining Israel's main supporter and benefactor.